General Comments

The manuscript submitted by Cuesta-Valero et al. considers continental heat storage and determines the contribution from three components. The analysis is important as it contributes to better understanding of the overall global heat balance by ensuring that all components are accounted for in the calculation of continental heat storage. The subject area is therefore appropriate for publication in ESD and would be of interest to its readers. The MS is also relevant to better estimates of the impact of climate change on the landmass. The MS has clear objectives and is generally well written with results and interpretations presented clearly. I don’t have any major concerns with the MS but I do have a number of comments that should be considered prior to acceptance for publication.

One of the key things that is done in the paper is the calculation of the heat in the ground that is utilized for phase change (latent heat) as ice in permafrost melts. However, the way the paper is written the authors seem to consider this separate from the subsurface (or ground) heat storage, which I found odd. Permafrost is a component of the ground (essentially a thermal condition of the ground) in cold environments so both the heat used to raise its temperature or for phase change when it thaws are components of the heat that is stored in the ground. It would seem that this is more an issue of the method that has been traditionally utilized to determine ground heat storage. Analysis utilizing subsurface temperature profiles only considers conduction in the estimate of ground heat fluxes. As ground temperatures approach 0°C in permafrost, heat is utilized for phase change of any ice in the ground rather than raising the temperature and little change in temperature over time is observed in ground temperature profiles (as discussed in Romanovksy et al. 2010; Smith et al. 2010). Lack of consideration of the latent heat effects therefore means that ground heat storage determined considering only conduction would be underestimated. It would make more sense for the authors to say that they are refining the estimates of ground heat storage by addressing a limitation of the method traditionally used by considering the latent heat utilized for phase change in the estimates.

The authors do not mention the role of other modes of heat flux in the ground such as convection. Heat transfer associated with water movement (advection) such as infiltration of precipitation and snow melt or subsurface water flow may also influence the ground thermal regime (see for eg. Douglas et al. 2020; Neumann et al. 2019; Phillips et al. 2016; review of Smith et al. 2022b also discusses this). As permafrost thawing occurs, subsurface water flow becomes more important. Is lack of consideration of this mechanism of heat flow also a limitation of the method used to determine ground heat storage?

I have a number of additional comments (see below) for the authors’ consideration in preparing the revised manuscript. These comments identify where further clarification or information may be required. Suggestions for editorial revisions have also been provided.

Specific comments (keyed to line number)

L31 – See comment above – permafrost is the ground (earth material) so its thaw is a component of subsurface heat storage.

L32 – Suggested revision: “ The ground accounts for ~90% of…..”

L41 – What is included in “cryosphere”? Permafrost is a component of the cryosphere but it is treated separately in this paper.

L53 – Permafrost includes soil and rock. Since there can be water within rock, phase change can also occur in frozen rock (even if the amount is small compared to soils).

L55 – replace “underline” with “underlie”

L55 – Note Obu (2021) determines the equilibrium permafrost distribution so it does not consider permafrost that formed under a colder climate and still persists today. For example, permafrost in peatlands in the southern portion of the permafrost regions formed under colder conditions and is preserved due to the insulating properties of peat. Also, permafrost can be quite thick in the Arctic and it can take a century or more to completely thaw so that relict permafrost continues to exist as climate warms.

L56 – It is important to note that these are average values of warming based on several sites (I believe Biskaborn 2019 gives a range).

L59 – Misleading/incorrect statement. These simulations only consider the upper 2-3m of permafrost rather than its total vertical extent, which may be 10s to 100s m. These values therefore do not refer to complete loss of permafrost from this area (i.e. refer to thaw being more than 2-3m over this area).

L61 – Permafrost is frozen ground so permafrost heat uptake is ground heat uptake. Until it thaws, the heat storage would be accounted for by the methods (inversion of temperature profiles) utilized to determine ground heat storage.

L66 – What is meant by recent times? It would be clearer to give the time period over which this reduction occurred.

L67 – suggested revision: ‘ ….going to continue throughout the 21^st century…:

L79 – should this be “deep subsurface temperature profiles”

L87 – replace “in” with “of”

L89 – revise to “slope of this regression line” (or best-fit line)

L99-100 – If the time for temperature changes at the surface to reach a given depth depends on the thermal properties, how does truncating to the same depth yield the same temporal reference if thermal properties are variable?

L131-134 – I may have missed something here  - how are the results from point-based measurements applied to the entire area considered. In figure 2a, heat storage is shown for points that are not uniformly distributed with very large areas not represented. It isn’t clear how the point-based data are extrapolated to the larger area or what other information may be utilized especially give the large areas with no data.

L136 – Isn’t it more correct to say that the heat input to the subsurface is utilized to melt ground ice as permafrost temperatures approaches 0°C?

L140 – Do you mean the surface offset which is the difference between mean annual air and ground surface temperatures and is influenced by snow cover. The thermal offset refers to the difference in temperature between the ground surface and the top of permafrost, which (if equilibrium conditions exist) depends on difference between frozen and unfrozen thermal conductivity (See for e.g. Riseborough et al. 2008).

L143 – What about rock – permafrost includes rock which can contain ice.

L179 – How is depth determined?

L165-199 – Lakes can form or drain in the Arctic due to permafrost thaw. Is the change in surface water distribution due to thermokarst processes considered or is this a limitation to heat storage estimates?

L220 (also elsewhere in paper including L223) – See earlier comments. Permafrost heat flux, if thaw is not is not occurring (this will be the case where temperature below melting point of ice in the ground) will be considered in the estimates of subsurface storage determined utilizing subsurface temperature records. It is only when thaw occurs in warmer permafrost at temperatures near 0°C that latent heat needs to be considered in addition to conduction.

L235 – Where around Hudson Bay? There was cooling in the eastern Arctic including northern Quebec into the 1990s – is this the reason for the lack of heat gain in this area?

L267 – Why isn’t the Tibetan Plateau included given it is a fairly significant area. Permafrost in this region is generally warm so latent heat effects are important.

L275-276 – It is important to indicate here that the estimate of ground heat flux needs to consider non conductive heat flow (i.e. address limitations) to improve estimates. The MS makes progress in addressing this limitation by considering the latent heat associated with phase change as permafrost thaws.

L280-300 – This section is OK but most of this has been well covered in other publications so nothing really new here.

L280-285 –Other implications of ground warming and permafrost thaw are impacts on landscape processes and stability, changes to surface water distribution and increase in subsurface water flow. These impacts can also have feedbacks to the ground thermal regime with further impacts on carbon feedback.

L288-290 – This is really an issue of landscape change associated with thawing of ice-rich permafrost (such as subsidence, thaw slumps), which is abrupt or sudden, exacerbating permafrost thaw – with geomorphic change such as slumps and other slope failures the upper boundary changes as material is removed (also lateral heat flow).

L293 – Do you mean “surpassing” rather than “trespassing”

L295-300 – Other impacts related to permafrost thaw (especially if ice-rich) include loss of bearing strength and ground settlement/subsidence with impacts on infrastructure; landscape instability including slope failures which can release sediment into water bodies with implications for water quality; impacts on integrity of contaminant containment facilities.

L301-303 – more evaporation?

L325-335 – There are several recent ground temperature records in the permafrost regions (some results included in Smith et al. 2022b, Noetzli et al. 2022, Biskaborn et al. 2019 and other papers). These are generally at shallower depths (usually upper 20 m) than would be utilized for the inversion of ground temperature profiles that is utilized in the MS. However, these provide information at depths where latent heat effects are important.

L337 – This is not a new observation and the lack of ground ice information has been identified as a limitation in permafrost modelling in other papers (e.g. Smith et al. 2022b; O’Neill et al. 2020).

L347 – With respect to latent heat effects related to permafrost thaw, including the Tibetan Plateau is probably more important than permafrost zones of Antarctica given the rather dry conditions and the geology.

L358-359 – While the deeper subsurface is an improvement, the LSMs still have limitations with respect to representation of subsurface conditions including ground ice distribution.

L382 – As mentioned in previous comment there are borehole temperature measurements in permafrost and at some sites, there are moisture content measurements. There are also often observations of excess ice content when boreholes are drilled.

L385 – One of the issues in areas such as the Canadian Arctic is the remoteness and significant cost of drilling boreholes, especially deeper ones where specialized equipment needs to be transported to the site (see for e.g. Smith et al. 2022b). Most permafrost monitoring sites therefore are often located near communities, existing infrastructure, associated with resource development (hydrocarbon, mining) etc.

L392 – This is also discussed in Smith et al. (2022b) and O’Neill et al. (2020). There are also efforts to improve ground ice potential modelling and mapping – see for e.g. O’Neill et al. (2019)

Figure 5 – See previous comments regarding other implications of permafrost thaw such as impacts on infrastructure integrity. Landscape instability is a more inclusive term than ground subsidence.

References cited in comments

Douglas, T. A., Turetsky, M. R. & Koven, C. D. 2020. Increased rainfall stimulates permafrost thaw across a variety of Interior Alaskan boreal ecosystems. npj Clim. Atmos. Sci. 3, 28.

Neumann, R. B. et al. 2019. Warming effects of spring rainfall increase methane emissions from thawing permafrost. Geophys. Res. Lett. 46, 1393–1401.

Noetzli, J. et al. 2022. [Global Climate] Permafrost Thermal State [in "State of the Climate in 2022]; Bull. Am. Met. Soc. Supplement, 103 (8)

O'Neill HB, et al. (2020) Abrupt permafrost thaw and northern development: Comment on “Abrupt changes across the Arctic permafrost region endanger northern development” by B. Teufel and L. Sushama. Nature Climate Change 10:722-723

O’Neill, H. B., Wolfe, S. A. & Duchesne, C. 2019. New ground ice maps for Canada using a paleogeographic modelling approach. Cryosphere 13, 753–773. – See also O’Neill et al.

Phillips, M., et al. (2016). Seasonally intermittent water flow through deep fractures in an Alpine Rock Ridge: Gemsstock, Central Swiss Alps. Cold Regions Science and Technology, 125, 117–127. https://doi.org/10.1016/j.coldregions.2016.02.010

Riseborough D, et al. (2008) Recent advances in permafrost modelling. Permafrost and Periglacial Processes 19 (2):137-156. doi:10.1002/ppp.615

Romanovsky VE, Smith SL, Christiansen HH (2010) Permafrost thermal state in the polar Northern Hemisphere during the International Polar Year 2007-2009: a synthesis. Permafrost and Periglacial Processes 21:106-116

Smith SL, Romanovsky VE, Lewkowicz AG, Burn CR, Allard M, Clow GD, Yoshikawa K, Throop J (2010) Thermal state of permafrost in North America - A contribution to the International Polar Year. Permafrost and Periglacial Processes 21:117-135. doi:10.1002/ppp.690

Cuesta-Valero et al. provide a new estimate of continental heat storage including ground, inland waters and permafrost thawing. For continental heat storage, an update to the previous estimate (Cuesta-Valero et al. 2021) is provided. For inland waters and permafrost thawing, models are used to derive the estimates. I have some major reservations about their methodologies, listed below.

(1). The observation-based estimate for ground heat storage and model-based estimates for inland waters and permafrost thawing are merged together to provide the continental heat storage. I doubt if they can be put together, and then eventually be used in von Schuckmann et al. GCOS assessment (the other components are all observation-based).

(2). Uncertainty estimates for ground heat storage. In this study the uncertainty of the ground heat storage has been reduced by an order compared to their earlier estimate (for example line 200-205). The new estimate suggests a global land heat storage of 84.8 +/- 0.8 mWm-2 (previous estimate is 97+/-6). I found it hard to believe such a small error range, it is simply not possible. Remember you are using only ~1000 station data to represent the entire land, even previous error range of 6 is a likely underestimation. I can’t understand this small number and I don’t understand how this small number is derived given the dataset is basically the same with the previous version.

(3). Uncertainty estimates for permafrost thawing. Only the uncertainty related to the soil thickness and ice saturation are taken into account. However, I think another major error come from the model and climate forcing. For example, the use of Mk3L and ERA-Interim, the errors/biases will definitely propagate into the estimate of this study. I have no idea how to resolve this, as it is related to the fundamental choices of this study: using models and reanalysis to drive the their estimates.

(4). Uncertainty estimates for inland waters. Is the ensemble spread used to estimate the uncertainty of heat storage in inland waters? If so, it is fundamentally different from the other two components, i.e. the assumption underlying this method is: model difference (whatever caused the difference) can fully represent the uncertainty. Such assumption is likely wrong as there are always common model biases. And such assumption is clearly different from the assumption for your permafrost thawing and ground heating uncertainty estimate, so they can not be simply added up, simply physically meaningless.

(5). How the final estimate of land heat storage uncertainty been derived? Are you assuming independency of the three components? Are they independent?

(6). Line 219: Please explain why “this large interannual variability is explained by the smaller surface of global lakes and reservoirs in comparison with the global land and permafrost areas”?

(7). Line 257. The total land heat storage is 23.9+/-0.4 ZJ. The error range is too small to believe. Look at Fig. 1a, there are only several places with observations, and the spatial variability is large (that means you need more data to resolve these variability), so I don’t think the uncertainty can be so small. The uncertainty estimate should be better documented in this study, and any revision should be carefully assessed and validated.

To proceed (avoid rejection of this paper), I recommend the authors not putting the the estimates for the three estimates toghether, just presenting them separately, making a point that permafrost and lakes might be important in EEI, which is the best the authors' can do.. I disagree to put them together because some are model-based estimates, and the uncertainty etsimates are apparant very weak.

In this manuscript the authors evaluate the continental heat uptake since 1960. It is an update of their previous work published in von Schuckmann et al. 2020. Compared to von Schuckmann et al. they made 3 changes in their estimate: 1) they changed their method to estimate the ground heat uptake from subsurface temperature profiles 2) they added an estimate of the permafrost heat uptake with a permafrost model and 3) they added an estimate of the lake, reservoir and river heat uptake with a global lake model forced by historical simulations of Earth System Models (ESM). The authors find a total continental heat storage of 23.9±0.4 ZJ since 1960 which is consistent with von Schuckmann et al. estimate of 24 ZJ since 1960. But this consistency is by chance. Indeed, the authors actually find a ground heat uptake that is significantly smaller than von Schuckmann et al. 2020 by 12mW.m-2 and the difference in ground heat uptake is compensated by the addition of the permafrost heat uptake and the inland water heat uptake estimates.

The manuscript is clear and well written. It deals with an important question which is the distribution among reservoirs of the excess of heat gained by the climate system in response to greenhouse gases emissions.  The distribution of heat among the Earth reservoirs at interannual and longer time scales is driven by the different heat capacities of the different reservoirs. The heat capacities of the reservoirs show very marginal changes with climate change thus the distribution of heat in the climate system is the same over time as it warms. It is important to estimate the distribution of heat among the Earth reservoirs to determine where the heat is actually located and what are the places of the world that are the most impacted by global warming. This is also a good indicator of current global warming and its distribution. As such, it is useful to derive the land heat uptake in order to raise public awareness. The work in this manuscript helps in this objective. In particular I find interesting the tentative estimate of the permafrost heat uptake. Permafrost heat uptake is an important indicator of the changes in a key place for the future of the climate system. It could  definitely be an interesting indicator to raise public awareness. 

Concerning the results of this paper, I find they are disappointing for three main reasons

First the authors find a ground heat uptake that is not consistent with their previous estimate in von Shuckmann et al. 2020 although they have used the same subsurface temperature profiles and the same inversion method. The significant difference between their previous estimate and the current estimate comes from the aggregation technique. But the confidence in the aggregation technique is not evaluated in the manuscript. So, we don’t know why the estimate of ground heat uptake is so sensitive to the aggregation technique and what should be done to tame down this high sensitivity. We don’t know either which aggregation technique should be trusted and thus which estimate of the ground heat uptake should be trusted:  the one that is propsoed in this manuscript or the previous one from von Shuckmann et al. 2020? More analysis are needed here to determine the confidence in the ground heat uptake estimate and explain the causes for the differences among the different estimates

Second, the authors estimate the inland water heat uptake from models only. They do not use any observations or reanalysis (even the forcing of the global lake model is coming from ESMs). If the objective of continental heat uptake estimates is to “inform about future warming and climate change as well as to understand the future consequences for society and ecosystems associated to continental heat gains »  as the authors claim, then it does not make sense. Climate model projections are not informed by their own simulations of the historical period. They are informed by comparison against independent observations retrieved from the real world. So, to support their objectives the authors should provide an estimate of the  inland water heat uptake that is derived from observations in a way or another (using forcing from reanalysis for example?)

Third I find that the uncertainty estimates are in general largely overlooked over the whole paper. In the case of the ground heat uptake, we are left at the end of the paper with a new estimate of the ground heat uptake with a very low uncertainty range (±0.8mW.m-2). This small uncertainty range only accounts for errors in the thermal diffusivity, errors in  the thermal conductivity and errors in the reference profile (through the bootstrap approach). But it does not account for any sources of systematic uncertainty such as the poor and inhomogeneous distribution of the subsurface temperature profiles. Given the high sensitivity of the ground heat uptake estimate to the aggregation technique, the poor distribution of subsurface data is certainly the dominant factor of uncertainty here. Thus the very small uncertainty range of ±0.8mW.m-2  is dubious. In the case of the permafrost heat uptake the uncertainty range does not account for many sources of systematic uncertainties as well. In particular the estimate is done with a unique permafrost model. Permafrost models show very large differences. At least, the use of another (or several) model would give insights on the level of this potentially large source of systematic uncertainties. In the case of the inland water heat uptake there is simply no information on how the uncertainty is derived.

For these reasons I think the paper is not ready for publication as it is. I think  it needs a substantial amount of work to answer the important points I raised before.

I add below a list of additional comments

 l46: what do you mean by “consistently”

l53:”high latent heat of fusion”: high compared to what?

L95: the Xibalba logs are poorly and in-homogeneously distributed. Have you estimated the biases that could be caused by this  in-homogeneous distribution? This is probably a leading source of uncertainty. You should at least estimate the order of magnitude of this source of systematic uncertainty and acknowledge it in the paper.

L102: the reference period for the calculation of the quasi equilibrium is precisely during the little ice age when land heat uptake was probably negative. This is potentially an issue for the inversion as it may bias high the anomalies with respect to the quasi equilibrium (since the quasi equilibrium you chose was a cold transient response to the little ice age rather than an equilibrium). Have you analyzed this possibility ? Do you have an idea of the potential error induced by the fact that the reference period is during the little ice age rather than during an equilibrated period?

L130: same remark as for l 95: the bootstrap approach quantifies the uncertainty due to errors in the thermal diffusivity, errors in  the thermal conductivity and errors in the reference profile. But what about the systematic errors coming from the in-homogeneous and poor distribution of profiles? This source of uncertainty probably dominates over the others. Can you elaborate on this? Provide a first estimate of this systematic error?

L145: the permafrost heat storage is derived from a model. But to which extent can we trust this model to represent the actual Permafrost? You do not provide any information on the validation of the model against observations. What confidence do we have in such a model?

L160: you are using a unique permafrost model. What about comparing against other independent models to get insight on the amplitude of potential sources of systematic uncertainty related to your model?

L172: why not using a forcing from reanalysis rather than ESM?  This would be much closer to the real world. You claim further that the heat uptake estimate is important to inform projections of the future climate. If so, you need to get observational estimates of the heat uptake rather than model estimates. I don’t understand the rationale here to use ESM forcing rather than reanalyses forcing

L199: How do you account for river depth?

L199: how do you compute the uncertainty  of your inland water heat uptake estimate?

L204: the new uncertainty range is one order of magnitude smaller!!! This is huge! Especially for uncertainty. How do you explain that?

L204: the very small uncertainty of the present study is such that your result is inconsistent with your previous estimate in von Shuckmann et al. How do you explain that? The inconsistency between both results means that one or the other or both estimates are wrong!! Which one is wrong then? The present study estimate or your previous study estimate? The paragraph L202 to l212 recall the method used in von Shuckmann et al. 2020 and the method used here to aggregate the data. But it is inconclusive on which aggregation method should be trusted. Since the two methods yield inconsistent results, we need to understand where the problem is, which number should be trusted and why we should trust it rather than the other.

L215: I find dubious that the different inversion technique and the different number of vertical profiles are enough to explain a change of the ground heat uptake by a factor 2 between Beltarmi 2002 and this study. Either there is a misunderstanding of the real causes for the difference between both estimates or it means  that land heat uptake is highly sensitive to the number of vertical profiles. It brings me back to my previous question: is there an important bias due to the poor and in-homogeneous sampling of the vertical profiles. A good test would be to take the same profiles as Beltrami 2002 and re estimate the land heat uptake with the inversion developed here and check whether you find the same result

L262-264 your new result agrees with your old result but for wrong reasons!! It is because you were biased in the ground heat estimate and here the bias is compensated by the new reservoirs you are adding in  (permafrost and lakes). The right conclusion is that you find a ground heat uptake that is significantly different from the previous one . You should acknowledge that clearly and explain why. Can you elaborate on that?

L270 paragraph 4: I don’t understand the point of this paragraph. Indeed we know that land heat uptake has numerous impacts on society and ecosystem. But it does not mean we need to estimate the land heat uptake to anticipate those impacts. In practice impacts on society and ecosystem are not derived from estimates of the land heat uptake. They are rather estimated from the output of climate models which use as input CO2 concentrations and which tune their model against surface temperature and global EEI at TOA. So, in which way estimating land heat uptake will help to improve climate models and anticipate impacts on society or ecosystems. We should rather focus on improving the land surface models that are embedded in climate models, shouldn’t we?

The only interest I see in estimating land heat uptake or permafrost heat uptake is to derive indicators for public awareness. Is that what you want to do? If so, you should state it clearly

L322 : I have the same remark: I don’t see how the magnitude of land heat uptake inform on future warming and climate change. Futur warming and climate change are given by climate models and climate model just don’t work with land heat uptake. So please elaborate to explain what you mean here

L325: An interest I see in estimating land heat uptake is to derive an observational benchmark against which climate model could be validated. But in this case you would need to derive observation only estimates of land heat uptake. That would be probably more suitable to the objective of informing projections of future warming